Correlating objects, or correlation, is a process of comparing tracks from different radars to determine which tracks are duplicate tracks. Tracks can include data sensed about an object or target by a sensor such as radars, global positioning systems, laser target designators, seismic sensors, and the like, and the data can include the positions and velocities of planes, ships, troops, or other targets. The goal of correlation is to reduce the number of redundant or duplicate tracks so that a theater accurately depicts the unique objects present within the area of interest. Correlation requires substantial statistical analysis in many applications since each radar tracks the position of the object with respect to an unknown or imprecisely known location and orientation, especially in applications wherein one or more radars may change positions over a period of time. A global positioning system and compass system at each radar estimates the location and orientation within a margin of error, however, it is a relatively rough estimate, too rough for many applications.
The output of a correlation system provides tracks to a system to model the theater, which typically encompasses a greater geographical area than the range of an individual radar. The size and accuracy of the theater, however, is limited by the amount of data that can be processed. For example, a radar can drop a target or object on occasion. The problem of dropped targets is likely resolved by overlapping the sensor range with more than one radar. However, overlapping the sensor range with two radars produces twice the data to process for the overlap and can lead to association ambiguities that must be resolved.
Computers, such as Cray computers, reduce the number of duplicate tracks of objects within the theater by cross-correlating the positions and velocities of each track of a first radar against the positions and velocities of each track of a second radar, wherein the range of the second radar overlaps part of the range of the first radar. After cross-correlating positions and velocities of the tracks, the correlation ratings or costs are compared to determine which tracks from the first radar match tracks from the second radar. Finally, the costs to pair or match each track of the first radar with a track from the second radar are compared with a reference cost to determine whether the probability that the tracks correspond to the same object is high enough to exclude one of the tracks from the theater. Even at this point, ambiguities can exist; there might be more than one possible association for one or more targets. In this case, we are left with what is known as the sparse matrix assignment problem. For example, the Cray computer receives the position and velocity of a plane from the first radar transformed to absolute coordinates. The global coordinates are determined based on a position and azimuth from a global positioning system and compass system for the first radar. The Cray computer also receives a position and velocity for the same plane from a second radar in absolute coordinates. Error involved in the transformation cause the tracks to indicate different positions for the same target. Using statistical techniques founded in maximum likelihood theory, the Cray computer compares the position and velocity of each track from the first radar to each track of the second radar to determine which tracks are close enough to label as duplicates. However, by comparing tracks of objects at one moment in time and individually, error sources such as noisy data or temporal sampling mismatches cause current systems to incorrectly match tracks. Further, the computational demands to associate each track individually is significant and increases significantly with the number of tracks to compare and the number of radars that overlap.
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